Figure 1: Conceptual design route of ME-active spin cluster.

(a,b) Schematic illustrations of monopolar (a) and magnetic quadrupolar (b) vortices in the absence and presence of a magnetic field B (solid black arrow). The red solid, blue open and blue solid arrows represent the orientation of spin, the local electric polarization p and macroscopic electric polarization P, respectively. (c,d) A square planar cluster composed of ferromagnetically (FM) (c) and antiferromagnetically (AFM) (d) coupled four spin plaquette, respectively. Blue and black balls represent the transition metal (TM) ions (n=1–4) and ligands, respectively. (e,f) Square cupola clusters after buckling the cluster in c and d, respectively. The FM square cupola cluster in e has the monopole moment while the AFM square cupola cluster in f has the magnetic quadrupole moment , where r_n is a position vector of the TM ion n from the centre of the four TM ions and S_n is a spin moment.